1,595 research outputs found
Quasi-local charges and asymptotic symmetry generators
The quasi-local formulation of conserved charges through the off-shell
approach is extended to cover the asymptotic symmetry generators. By
introducing identically conserved currents which are appropriate for asymptotic
Killing vectors, we show that the asymptotic symmetry generators can be
understood as quasi-local charges. We also show that this construction is
completely consistent with the on-shell method.Comment: 19 pages; v2 typos fixe
Thermodynamic Volume and the Extended Smarr Relation
We continue to explore the scaling transformation in the reduced action
formalism of gravity models. As an extension of our construction, we consider
the extended forms of the Smarr relation for various black holes, adopting the
cosmological constant as the bulk pressure as in some literatures on black
holes. Firstly, by using the quasi-local formalism for charges, we show that,
in a general theory of gravity, the volume in the black hole thermodynamics
could be defined as the thermodynamic conjugate variable to the bulk pressure
in such a way that the first law can be extended consistently. This, so called,
thermodynamic volume can be expressed explicitly in terms of the metric and
field variables. Then, by using the scaling transformation allowed in the
reduced action formulation, we obtain the extended Smarr relation involving the
bulk pressure and the thermodynamic volume. In our approach, we do not resort
to Euler's homogeneous scaling of charges while incorporating the would-be
hairy contribution without any difficulty.Comment: 1+21 pages, plain LaTeX; v2 typo fixed and references adde
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